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Abstract: This project focuses on image deblurring and centerfinding for astronomical optical navigation. Optical navigation (OPNAV) has been in use in multiple spacecraft for many years, and is an important component of spacecraft navigation. However, OPNAV deals with images which are blurry and contain noise, so image processing is an integral part of OPNAV. This project seeks to solve traditional OPNAV problems with a new approach: deblurring using inverse matrix linear algebra, paired with centerfinding techniques. To accomplish this we use filtering, regularization, and sparse inversion methods. A discussion of both visual results and quantitative results is given, and of which methods perform best in each category. Then, possible conclusions, as well as future directions are discussed.

Biographical Information: Liam Coulter is the CAM Student Research Award winner for summer 2016. Liam graduated from the University of St. Thomas in 2017 with a major in math, and minors in engineering and philosophy. He is currently in his first year of a math Ph.D. program at Colorado State University. During his Ph.D. he hopes to research applied mathematics, in a field related to linear algebra, applied topology, or inverse problems. He enjoys hiking, climbing, and playing guitar in Colorado (when he’s not doing homework for real analysis!) He also enjoys the fact that the yearly low temperature in Fort Collins is a balmy 15 degrees fahrenheit, but recognizes that CSU doesn’t have skyways or tunnels between buildings, so it’s unclear who is the real winner.